Stability of bistable traveling wavefronts for a three species competitive-cooperative system with nonlocal dispersal

This paper is concerned with the dynamic behaviour of a three species competitive-cooperative system with nonlocal dispersal, which describes two species are cooperating with each other and competing with the third species together. Firstly, by using the theory of monotone semiflows, we obtain the existence of bistable traveling wavefronts, which reflects that two cooperative species are invading the third one along the x-axis. We then investigate the global asymptotic stability of these wavefronts by applying a dynamical systems approach and constructing some suitable super-sub solutions. And we also obtain that such wavefronts are unique up to translation with the unique wave speed. In the end, we give the exact min-max representation of the unique wave speed by strict analysis.